help please physics, derivation...?

Question

what is the derivation of

a = g times m over m plus M

a= acceleration
g= gravity
m= mass
M = mass of the glider

explanation please thank you

Answer 1

a=gm/(m+M) or derivation in reverse

am + aM= gm

F(on mass m) + F(on mass M)= weight of m

I have no clue what was the original set up (a picture or description would be great) however it seems we have:

Frictionless table upon which a mass M (glider) is placed. A massless string is attached to the glider and over massles and frictionless pulley a mass m is attached and is freely hanging. The system is then released. The acceleration a of the system is the question.

Answer 2

The quantity m/(m + M) could be regarded as what is called a "reduced mass".....BUT.....the reduced mass is written as: mM/(m + M), where the overall units are mass, usually kilograms.

In your case the units cancel, which may be by design, but without knowing the context it's hard to guess.